Reflection between the foci of an ellipse ($AP+PB=2a$)

An ellipse is a constant sum of distances to its foci. Its outward normal vector is parallel to the sum of the two unit vectors pointing from the foci to a boundary point. The tangent is therefore equally inclined to the two focal lines. Reflecting an incident unit ray from one focus across this normal gives the direction toward the other focus. Every such one-reflection path has length $2a$, giving equal travel time in a homogeneous medium. Finite-wavelength wave focusing is limited by diffraction.